On conditional compactly uniform pth-order integrability of random elements in Banach spaces
The notion of conditional compactly uniform pth-order integrability of an array of random elements in a separable Banach space concerning an array of random variables and relative to a sequence of [sigma]-algebras is introduced and characterized. We state a conditional law for randomly weighted sums of random elements in a Banach space with the bounded approximation property, and we prove that, under the introduced condition, the problem can be reduced to a similar problem for random elements in a finite-dimensional space.
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Volume (Year): 55 (2001)
Issue (Month): 3 (December)
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